Combined GPS and Inertial Navigation System

By Andrew Aubry

Advised by

Dr. In Soo Ahn

Dr. Yufeng Lu

January 17, 2016

Electrical and Computer Engineering Department

Bradley University

1501 W Bradley Ave

Peoria, IL 61625

2

ABSTRACT

Highly accurate real time navigation has recently been made possible due to advances in

satellite and inertial navigation technology. GPS provides consumers access to inexpensive

methods of navigation, but is not always locally available. These outages can be mitigated

through the use of an Inertial Navigation System (INS) which uses dead reckoning instead of

external signals to compute the navigation solution. Advances in MEMS technology have

produced inertial measurement units (IMUs) that fit on integrated circuit chips, and greatly

improved portability. These MEMS sensors are highly susceptible to noise, which left unchecked

can cause severe drift in the navigation solution. The combination of an INS and GPS can

mitigate the drift, and combined with a linear estimator, the Kalman filter, can produce a viable

navigation solution. A system to collect IMU and GPS data was constructed. A strapdown

solution in MATLAB was also built. A Kalman filter was attempted but unsuccessfully

implemented.

3

ACKNOWLEDGEMENTS

I would like to thank my advisers, Drs. In Soo Ahn and Yufeng Lu, for all the help. The

final report is long overdue but my advisors were kind enough to wait patiently. My years at

Bradley have prepared me to meet the challenge of real-life problems and solve them. I also

thank the entire ECE faculty and staff for all their help during my study at Bradley University.

4

CONTENTS

I. Introduction ..................................................................................................................5

II. Inertial Navigation .......................................................................................................6

A. Complete Project Description ..................................................................................6

B. Inertial Navigation Background ...............................................................................6

C. Reference Frames.....................................................................................................7

III. Mathematical Development ........................................................................................9

A. Inertial Navigation System ......................................................................................9

B. Kalman Filter .........................................................................................................11

IV. System Setup and Equipment ...................................................................................12

A. System Design .......................................................................................................12

B. Inertial Measurement Unit .....................................................................................12

C. GPS ........................................................................................................................15

D. Data Logger Design ...............................................................................................16

V. Results .........................................................................................................................20

A. Data Logger ...........................................................................................................20

B. Inertial Navigation System ....................................................................................22

VI. Conclusion ..................................................................................................................24

VII. Appendix .....................................................................................................................25

A. IMU Data Log Sample ...........................................................................................25

B. GPS Data Log Sample ...........................................................................................26

References ...................................................................................................................27

5

LIST OF FIGURES

1. System Block Diagram ........................................................................................................7

2. Navigation Reference Frames ..............................................................................................8

3. Strapdown Inertial Navigation System ................................................................................9

4. VN-100 Attitude Heading and Reference System .............................................................14

5. uBlox EVK-5T GPS Unit ..................................................................................................16

6. Sparkfun Logomatic V3 Data Logger................................................................................17

7. Sample IMU Message ........................................................................................................17

8. Data Logger Initialization Flowchart .................................................................................18

9. Data Logger Main Routine Flowchart ...............................................................................19

10. Data Logger UART Interrupt.............................................................................................20

11. IMU and Data Logger ........................................................................................................21

12. Strapdown Solution Flowchart ..........................................................................................23

13. Strapdown Solution Drift ...................................................................................................23

LIST OF TABLES

1. VectorNav VN-100 Sensor Specifications (25 °C) ...........................................................14

2. Data Transmission Rates....................................................................................................15

3. uBlox EVK-5T Sensor Specifications ...............................................................................16

4. Final System Parameters ....................................................................................................21

5. Drift of Stationary Sensor Test ..........................................................................................23

6

I. Introduction

Recent advances in satellite and inertial navigation technology have made determining

position and attitude of a vehicle in real time a reality. The advent of GPS has provided

consumers with an inexpensive receiver for civilian navigation. Yet, there are occurrences where

GPS signals are unavailable. A different method, not subject to external signal blockage, must be

implemented in conjunction with GPS for navigation. The standard solution before GPS based

navigation was an Inertial Navigation System (INS). INS systems have been used for navigation

on many major projects including systems such as space vehicles and aircraft. An INS system

measures a body’s accelerations and angular rates to determine the position and attitude of the

vehicle. Recent advances in MEMS technology have brought cheap accelerometers to the

market. INS systems are an attractive choice where cost or available space are a concern.

The combination of GPS and INS allows for a highly accurate system that can mitigate the

drawbacks of both systems. An INS provides a description of the body’s accelerations and

angular rates, and can detect near instantaneous changes in orientation. Current MEMS sensors,

however, tend to be very noisy and can only provide short term stability for an INS solution.

Heavy statistical processing is required to make effective use out of the MEMS accelerometer

outputs [1]. A GPS system on the other hand, also provides an accurate vehicle position, but has

a much slower refresh rate than that of any typical INS. A coupled system can be constructed by

taking advantages of each system’s strength. Such system can survive frequent GPS signal

outages and improve position and attitude estimates of the vehicle [2].

7

II. Inertial Navigation

A. Complete Project Description

The project consists of four components or stages. These stages are the hardware and data

acquisition using a data logger, a fundamental navigation system, an advanced navigation

system, and finally an embedded system. The first system part is the hardware integration and

data acquisition system. Hardware must be chosen for accuracy and ease of interfacing. When

designing a combined navigation system, the timing of the measurements must be carefully

considered. Timing must be kept between individual sensor measurements, and also between

GPS and IMU measurements. The data acquisition system must have the ability to accurately

track and record the time at which a measurement is made in addition to the actual measurement.

The second component is the basic implementation of the combined INS and GPS system.

The system will be implemented in MATLAB, and utilize a Kalman filter for data fusion. GPS

position data from a GPS receiver is fed directly into the filter, and combined with the INS

solution to form a loosely coupled system. In order to model the MEMS based IMU sensors, a

linear Gauss-Markov process is to be used. These components provide the basis for a combined

GPS - INS navigation system, and allow for future expansion and refinement of the system. A

block diagram of these components is in Figure 1.

B. Inertial Navigation

Inertial navigation is a form of navigation which relies solely on the inertial measurements

and the initial position of a vehicle to determine position. Accelerometers provide the magnitude

of the acceleration on a vehicle body, which is then integrated to yield velocity and position. An

additional set of gyroscopes augment the accelerometers and allow the resolution of the

8

Figure 1: Complete system block diagram

directions of the accelerometers relative to a fixed axes or reference frame. Earlier inertial

navigation systems utilized a set of gimbaled accelerometers to maintain the orientation of the

measurements along fixed axes. The advent of more powerful embedded systems allowed the

measurement units to be fixed directly to the body, creating a strapdown inertial navigation

system (SINS).

C. Reference Frames

Multiple reference frames are used in a strapdown inertial navigation system (SINS). These

frames include the inertial frame, the earth frame, the navigation frame, and the body frame. The

inertial frame is defined by the axes Oxi, Oyi, and Ozi, with the origin at the earth’s center. The

axes Oxi and Oyi are non-rotating with respect to fixed stars, and the Ozi axis lies along the earth

polar axis. The earth axes’ origin is also located at the earth’s center, with the Oze axis lying

Navigation Computer

Navigation SensorsIMU Accelerations(Ax, Ay, Az)

Gyroscope Angular Rates

(Wx, Wy, Wz)

Magnetometer readings(Mx, My, Mz)

VectorNav

VN-100

uBlox EVK-5

GPS RecieverGPS Signal

Bundled Measurements

GPS Position and Time

Data Logger (10 kHz internal

timer)

INS

Kalman Filter

+

Error

Position and Attitude

Time Stamped Data

9

along the earth polar axis, and the Oxe axis pointing at the intersection of the equator and the

Greenwich Meridian. The earth frame rotates about the inertial frame at a rate of Ω, defined as

one revolution per sidereal day. The navigation frame is centered at the physical navigation

system with axes aligned with the directions of north, east and the local vertical (down). Finally,

the body frame is also located at the navigation system and coincident with the body’s roll, pitch,

and yaw axes. [3] An illustration of these frames relative to a globe is below in Figure 2.

Figure 2: A representation of relative navigation frames used for inertial navigation [3]

The navigation frame is the primary frame of operation for a strapdown inertial navigation

system. Measurements from the strapdown system components are taken from the body frame

and must be transferred to the navigation frame. Additionally, the Coriolis Effect and local

gravity forces are known in the earth and inertial frames respectively and must be transformed

10

accordingly. The translation of the navigation components is accomplished using methods that

include a direction cosine matrix and a quaternion. A block diagram depicting the strapdown

solution is shown in Figure 3.

Body Mounted Accelerometers

Body Mounted Gyroscopes

Resolution of specific force

measurements

Attitude Computer

Coriolis Correction

Navigation Computer

Gravity Computer

Σ Σf b

ωbib

Cn

b

f n

gn

Initial Attitude

Estimates

Initial Attitude

Estimates

Position and Velocity Estimates

ωnie + ωn

en

Figure 3: Block diagram of the navigation solution computed in the navigation frame [3]

III. Mathematical Development

A. Inertial Navigation System

The reference frame chosen for the strapdown solution is the Navigation Frame, also known

as the North-East-Down frame (NED). The solution for the navigation frame is primarily drawn

from [3]. The development of the strapdown requires vector and matrix notation, so let matrices

be distinguished with upper-case bold font, and vectors denoted as lower-case bold font. A

superscript on a vector or matrix signifies the current frame of navigation. When operating in the

END frame, the navigation equation is expressed by:

𝒆𝑛 = 𝑪𝑏

𝑛𝒇𝑏 − (2𝝎𝑖𝑒𝑛 + 𝝎𝑒𝑛

𝑛 ) × 𝒗𝑒𝑛 + 𝒈𝑙

𝑛 (1)

11

Where the components of the equation are defined by the following:

𝒗𝑒𝑛 = [𝑣𝑁 𝑣𝐸 𝑣𝐷]𝑻 (2)

Representing the velocity with respect to Earth in the NED frame, with the components of

velocity in the north, east, and local down directions. The accelerometers of the inertial

measurement unit return the specific force vector, measured in the local body frame:

𝒇𝑏 = [𝑓𝑥 𝑓𝑦 𝑓𝑧]𝑻 (3)

In order to resolve the specific body forces into the navigation frame used in the solution, the

direction cosine matrix, 𝑪𝑏𝑛, is utilized. The direction cosine matrix is comprised of Euler angles

to generate a rotation about the roll, pitch, and yaw axes in order to resolve the body frame

components into navigation frame components. Next, the two rotation components are composed

of the transport rate, 𝝎𝑒𝑛𝑛 , and the turn rate of the Earth in the navigation frame, 𝝎𝑖𝑒

𝑛 :

𝝎𝑖𝑒𝑛 = [Ω cos 𝐿 0 −Ω sin 𝐿]𝑇 (4)

The transport rate represents the turn rate of the local frame with respect to the Earth-fixed

frame:

𝝎𝑒𝑛𝑛 = [𝑙 cos 𝐿 − −𝑙 sin 𝐿]𝑇 (5)

The variables 𝐿, 𝑙, ℎ, and 𝑅0 represent the latitude, longitude, altitude, and radius of the earth

respectively. The local gravity vector, 𝒈𝑙𝑛, is the final component of the navigation equation and

is composed of the gravitation attraction of the earth,𝒈, and the centripetal acceleration of the

earth:

12

𝒈𝑙𝑛 = 𝒈 − 𝝎𝑖𝑒 × 𝝎𝑖𝑒 × 𝑹 = 𝒈 −

Ω2(𝑅0+ℎ)

2(

sin 2𝐿0

1 + cos 2𝐿) (6)

In order to keep the resolved force components up to date, the direction cosine matrix is updated

using the equation:

𝑏𝑛 = 𝑪𝑏

𝑛𝛀𝑛𝑏𝑛 (7)

Where 𝛀𝑛𝑏𝑛 is the skew symmetric form of the body rates in respect to the navigation frame,

𝛚𝑛𝑏𝑛 . Because the body frame also rotates about the earth’s axis and therefor the inertial frame,

the gyroscope measurements are represented by 𝛚𝑖𝑏𝑏 , and are converted to navigation rates by:

𝛚𝑛𝑏𝒃 = 𝛚𝑖𝑏

𝑏 − 𝑪𝑛𝑏[𝝎𝑖𝑒

𝑛 + 𝝎𝑒𝑛𝑛 ] (8)

To compute an equivalent direction cosine matrix, the quaternion may be used. The quaternion is

an attitude representation that utilizes four parameters to represent a transformation by a single

rotation about a vector defined with respect to the reference frame. The quaternion propagates

through time by the equation:

𝒒 = 1

2𝒒⨂𝒑 (9)

Where

𝒑 = [0 , 𝝎𝑛𝑏𝑏 𝑇

]𝑇

(10)

B. Kalman Filter

13

In order to compensate for the noisy measurements of the inertial measurement unit and

integrate the measurements from the GPS, a Kalman filter is used. The Kalman filter is a set of

algorithms that are categorized as optimal state estimators, and is based on minimum mean-

square error filtering with state space methods. Using a model of the dynamic system, combined

with measurements of the system output, the Kalman filter is able to estimate the current internal

states of a system. The Kalman filter is a discrete time algorithm. The development of the

Kalman filter here is provided by [4] and [5]. A system is represented by its states and outputs:

𝒙𝑘 = 𝑭𝑘−1𝒙𝑘−1 + 𝑮𝑘−1𝒖𝑘−1 + 𝒘𝑘−1 (11)

𝒚𝑘 = 𝑯𝑘𝒙𝑘 + 𝒗𝑘 (12)

With 𝒗𝑘 and 𝒘𝑘 representing Gaussian white noise, 𝑯𝑘 the observability matrix, and 𝑭𝑘 the

plant dynamics. Using an initial estimate of the system, 𝟎−, and an initial error covariance, 𝑃0

−,

an iterative process can be followed to estimate the internal states at discrete time points. Using

the initial estimates, the Kalman Gain, 𝑲𝑘, can be computed:

𝑲𝑘 = 𝑷𝑘−𝑯𝑘

𝑇(𝑯𝑘𝑷𝑘−𝑯𝑘

𝑇 + 𝑹𝑘)−1 (13)

Using this gain, an a posteriori estimate of the current state can be found:

𝑘+ = 𝑘

− + 𝑲𝑘(𝒚𝑘 − 𝑯𝑘−) (14)

With the new estimate of the current states, a new covariance can be found for the current

estimate:

𝑷𝑘+ = (𝑰 − 𝑲𝑘𝑯𝑘)𝑷𝑘

− (16)

14

Finally, using the current state estimate and covariance, a priori values for the next iteration can

be calculated as:

𝑘− = 𝑭𝑘𝑘

+ + 𝑮𝑘𝒖𝑘 (17)

𝑷𝑘+1− = 𝑭𝑘𝑷𝑘

+𝑭𝑘𝑇 + 𝑸𝑘 (18)

The Kalman filter presented here is a linear estimator. Use of this solution requires a

linear system, which may not be present in an INS / GPS system. Another whole set of filters

that overcome the linear requirement of the Kalman filter, and are classified as nonlinear filters.

These nonlinear filters include adaptations of the Kalman filter including the unscented Kalman

filter and the extended Kalman filters, as well as filters such as particle filters and batch filters.

When properly tuned for a system, these filters can achieve a much higher degree of accuracy

than the linear Kalman filter. For this project, only the linear Kalman filter presented above is

explored.

IV. System Setup and Equipment

A. System Design

To achieve a fused sensor system, the GIN system consists of three major components: the

navigation sensors, the data logger, and the navigation computer. A diagram of these components

was presented in Figure 1. The development of the project followed a natural progression from

the navigation sensors, to the data logging unit, and finally the navigation computer. The data

logger interfaces with both sensors using a Universal Asynchronous Receiver/Transmitter

(UART) communication setup. UART communication scheme transmits bytes of data in

sequential bits, which are then reconstructed at the destination UART chip. The byte nature of

15

UART allows for easy character transmission between modules. The first block, navigation

sensors, contains the IMU and GPS components.

B. Inertial Measurement Unit

The IMU selected for this project is the VectorNav VN-100 attitude and heading reference

system (AHRS). The VN-100 contains an IMU nine sensors, including three accelerometers,

three gyroscopes, and three magnetometers. Manufacturer specifications for the VN-100 can be

found in TABLE I, and an image of the sensor in Figure 4. The VN-100 utilizes a register system

for storing measurement messages.

TABLE I

VectorNav VN-100 Sensor Specifications (25 °C)

Accelerometer Gyroscope Magnetometer

Range ±2g X Y, ±6g Z ±500 deg/sec ±6 Gauss

Bias Stability 0.5mg X Y, 1.6mg Z < 100 deg/hour 0.125 mGauss

Nonlinearity < 0.5% < 1% < 1%

Figure 4: VN-100 Attitude Heading and Reference System

Because this system is an AHRS, a complete navigation solution can be obtained, however

only the raw data of the IMU is recorded and utilized. Both unfiltered and filtered data are

available from the unit. The message selected for use is the uncompensated earth magnetic field

16

readings, accelerations, and angular rates. This data can be found in register 252. The VN-100

can be set to either synchronous or asynchronous output mode. In synchronous operation, an

external signal must transmit a read request to the VN-100, and the requested register values are

returned. For asynchronous operation, the VN-100 is configured to output a specified register at

a set frequency. The asynchronous output frequency and register can be changed using a separate

control register. A list of asynchronous output frequencies is available in TABLE II. The VN-

100 supports either USB or UART communication. UART communication connects the IMU to

the data acquisition system, while the USB option provides convenient access to the board for

debugging purposes through VectorNav’s software.

TABLE II

Data Transmission Rate Information

Frequency (Hz) Minimum Baud (bps) Max SD Write Time (ms)

1 9600 426.0

5 9600 426.0

10 19200 213.0

25 57600 71.1

50 115200 35.5

100 230400 17.7

200 460800 8.88

C. GPS

The GPS unit selected for this project is the uBlox EVK-5T timing GPS, with manufacturer’s

specifications in Table III. The EVK-5T provides both USB and RS232 communication, and the

uBlox u-Center software allows for quick interfacing for configuring the unit. The NMEA and

UBX protocols are the two outputs available from the unit. NMEA is a standard ASCII based

GPS protocol, and provides access to information such as the geographic position, satellite

information, and dilution measurements. The UBX protocol is a uBlox proprietary format, and is

a binary format. The UBX protocol provides access to an extended set of measurements and

17

information from the GPS, but is not in ASCII format. While the raw GPS measurements may be

useful in future applications, the NMEA protocol provides the necessary information and works

well with the text logger since it is in ASCII format. The EVK-5T allows for synchronous or

asynchronous output, with an output frequency of up to 5 Hz. The selected output registers

include the geographic position information, satellite information, and range residuals. The

EVK-5T can be seen in FIGURE 5.

TABLE III

uBlox EVK-5T Sensor Specifications

Sample Rate 1-5 Hz

Tracking Sensitivity -160 dBm (Indoor)

GPS Type Galileo L1 (1575.42 Mhz)

Time to First Fix < 1 s

Channels 50

Assisted GPS SBAS, DGPS, Assist Now

Accuracy 2.5m (2.0m SBAS)

Figure 5: uBlox EVK-5T GPS Development Kit

D. Data Logger Design

Design considerations for the data logger included simultaneous logging of two UART

sources (DUART) at two differing output frequencies, text based logging, and low cost. The data

logger selected was the SparkFun Logomatic v3 Serial SD Data Logger. The Logomatic board

contains an ARM LPC2148, microSD support, 2 UART channels, and up to eight analog logging

channels. The Logomatic was selected for its dual UART channel, low cost, and high level of

18

flexibility. The SparkFun USB boot loader allows for firmware to be quickly changed by placing

an updated build file onto the microSD card via USB. Out of the box, the initial Logomatic

software provides single channel UART text logging, which saves the files to an SD card, which

can be retrieved either via a USB port on the logger, or by removing the SD card. The code for

the data logger is available for free from the manufacturer, utilizes open source libraries, written

in C, and is easily modifiable. The data logger is shown in Figure 6.

Figure 6: Sparkfun Logomatic V3 Serial Data Logger

Ideally, the frequency of the system is limited by the output frequency of the IMU, requiring

a sufficient data rate between the IMU and data logger. The message chosen for the IMU is the

uncompensated magnetic, acceleration, and angular rate measurement message. An example of

the IMU message is included below in Figure 7.

$VNCMV,-5.265888E-01,-7.150189E-01,+1.306738E+00,+6.423429E-02,+1.114974E-01,-

9.771467E+00,-1.795687E-01,+2.197948E-01,+8.457639E-02,+3.183125E+02*4A

Figure 7: Sample IMU Message

The message is broken into the following parts: message identification, three magnetometer

measurements, three accelerometer measurements, three angular rate measurements, and a

message checksum. Each message is 151 characters long, including the checksum and newline

19

characters. In binary UART communication, each symbol transmitted is a bit, meaning that the

baud rate and bit rate are equal. A tabulation of minimum baud rate for a given IMU output

frequency of the uncompensated measurement message is below in TABLE IV. The second data

transmission consideration is the recording of messages to the SD card. The standard

configuration of the data logger writes 512 character blocks at rate of 42.5 ms. The rate at which

the SD card can store is dictated by the serial peripheral interface (SPI) clock. Also included in

Table II is the maximum time a character array has to be written. The initialization routine for

the data logger, as well as the main software loop can be seen in Figure 8 and Figure 9

respectively.

20

Enter Main Program

END / Logger Reset

Initialize:- system clock- FIQ routine- FAT storage

- Logging functions- Timer

Create new log files- IMU- GPS

Open files

Call Action mode

(continous loop)

Initialize UART 0 and UART 1

Figure 8: Initialization routine for Logomatic data logger

21

Start

Enable Timer

Is lower IMU character array

ready?

Is upper IMU character array

ready?

Is lower GPS character array

ready?

Is upper GPS character array

ready?

Write lower array to IMU file on SD

Write upper array to IMU file on SD

Write lower array to GPS file on SD

Write upper array to GPS file on SD

Has stop button been

pressed?

Yes

No

No

Yes

Yes

No

Yes

No

Have less than 512 IMU characters been

received?

Have less than 512 IMU characters been

received?

Write upper array to IMU file on SD

Write lower array to IMU file on SD

Clear lower IMU array flag

Clear upper IMU array flag

Clear lower GPS array flag

Clear upper GPS array flag

Write upper array to GPS file on SD

Write lower array to GPS file on SD

Flash status lights

END

Figure 9: Main software loop of Logomatic data logger

An additional component of the data logger is time stamping the values that are received.

Accurate timing data must be maintained in order to later correlate the INS and GPS data in post

processing. Additionally, the time interval of the IMU messages are needed for the integrations

performed in the INS. On the data logger, incoming characters are handled via two 512 character

arrays. The two arrays alternate between storing received characters and writing to the SD card.

When a character is received, an interrupt service routine is called by the UART interrupt and

vectored to. This routine handles the character and returns it to the array. For time stamping

purposes, a timer at a frequency 10 kHz runs in the background of the data logger chip. When a

22

new line character, ‘$’, is detected, the timer value is grabbed, converted to a string, and

appended to the output array. Because of the 512 character limit on the arrays, overflow must be

handled accordingly. The UART interrupt service routine flow char is below in Figure 10.

ENTER UART ISR

Is the char a ‘$’?

Grab timer value

Convert timer to string

Set length = string length

END

Yes

Is the char a ‘*’?

Enter a ‘,’ into write array

Enter character to write array

Array length is equal to 1 char

No

Yes

Append char to output array

Are there remaining chars?

Did the received count start <= 511 and end

>=512?

Increment output and received counters

Is the received count < start

count?

Set lower array flag fullYes

Yes

No

No

No

Set upper array flag full

Yes

No

Figure 10: Interrupt service routine for handling UART characters on Logomatic data logger

V. Results

A. Data Logger

The first iterations of the data logger design focused primarily on interfacing solely with the

IMU as it is run at much higher frequencies than the GPS. The limiting factor of the system data

frequency was the SD write speed of the data logger; at frequencies higher than 50 Hz from the

IMU, messages would get dropped during the SD write process. This result was somewhat

23

expected, as the minimum SD write time of 42.5 ms was already exceeded by 6 ms at 50 Hz, and

24.8 ms at 100 Hz. The SD write speed is dictated by the SPI clock, and altering that frequency

impacts the write speed. Raising the frequency by a factor resulted in a write speed of

approximately 12.5 ms. This speed was measured by starting a counter before a write operation

of a full array, and stopping it once the operation was completed. This marked improvement of

about 30 ms beat the 17.7 ms write time needed to run the IMU at 100 Hz. The final data

collection system parameters are below in Table 5, with a picture of the system in operation in

Figure 11.

TABLE IV

Final System Parameters

Data Frequency Baud Format Message(s)

IMU 100 Hz 230400 ASCII Uncompensated earth magnetic field, accelerations, and angular rates

GPS 2 Hz 230400 ASCII Geographic position, satellites in view, range residuals

Figure 11: VN-100 IMU connected to the data logger

24

B. Inertial Navigation System

The raw text files generated by both the IMU and GPS were collected via the USB output of

the data logger and fed into MATLAB. A script was written to parse and store all variables

output from the sensors. Each line of data had simple formatting occur as characters were

received in the data logger to offset each component of the message with a standard delimiter, in

this case a comma. Using a delimiter allowed quicker and simpler parsing in MATLAB. The

script was set up to expect messages with specific formats and lengths; if a message was found

without not following that format, the message was marked as a bad measurement and replaced

with an average of the measurement before and after it. Errors on the IMU data sets showed up

approximately every 10,000 data points, or 100 seconds. These ‘hiccups’ in the data are

attributed to running the data logging and SD writing at higher speeds, as the problem was not

replicable at data frequencies lower than 25 Hz. The 1 in 10,000 bad data points was deemed

acceptable, and the bad point averaged as mentioned before.

For the first iteration of the strapdown solution, MATLAB code was generated to compute

the components of the solution, then combine and integrate the components to yield the Position,

Velocity, Acceleration and Jerk (PVAJ) of the body. The iteration of the process can be seen in

Figure 12.

The IMU was left to sit and record stationary data for fifteen minutes. This data was used to

measure the biases inherent in the accelerometers and gyroscopes. Two data sets were run

through the strapdown solution, the raw stationary data, and the same data set with the bias

subtracted off. The starting positions, ending positions, and change in positions of both data sets

can be seen in Table VI and Figure 13. Simply removing the biases of the sensors resulted in a

10X improvement over a fifteen minute period.

25

Figure 12: Flow chart of strapdown solution software iterations

TABLE V

Position Drift for 15 Minute Stationary Data Set

Start Latitude Start Longitude End Latitude End Longitude Position Change

Biased 40.6955° -89.6179° 40.5738° -89.4462 20.37 km

No Bias 40.6955° -89.6179° 40.7101 -89.6041 2.62 km

Figure 13: Drift in strapdown solution of 15 minute stationary solution

Start

Select IMU and GPS data files

Initialize Variables

Read initial geodetic

location - GPS

Initialize INS attitude

Read IMU Measurements

Valid Tranmission?

Copy previous measurement

No

Compute Earth rates

Yes

Compute body rates

Update angle object from

NAV computer

Compute specific force

Compute local gravity vector

Compute local n-frame

acceleration

Integrate acceleration

Convert local velocity to Lat/Long derivative

(geo_dot)

Integrate geo_dot

Update PVAJ object

End of File?

No

End

Yes

26

Despite the major improvement when removing the bias, a 2 km error is still unacceptable for

modern navigation. The next step to improve the accuracy of the navigation solution is to

integrate the position information measured by the GPS. The Kalman filter was not able to be

successfully implemented and unable to be used to incorporate the GPS position updates into the

INS position information.

VI. CONCLUSION

A navigation system combining an INS and GPS through Kalman filtering was proposed.

The system was composed of three major components, the navigation sensors, data logging unit,

and navigation computer. The data logging system has been successfully implemented on a

standalone logging unit, and has achieved simultaneous logging of IMU data at 100 Hz and GPS

data at 2 Hz. The data logging system has the ability to handle other IMU data rates also. The

received data all contain timestamps for aligning data between two different sets of sensors. The

SD write speed was found to be a limiting factor of the data acquisition system. A strapdown

solution was achieved in MATLAB. Data processed through just the INS component of the

navigation computer showed significant drift over a period of fifteen minutes for a stationary

body. Subtracting the average sensor biases showed a marked improvement, but still had an error

multiple orders of magnitude greater than necessary for modern navigation. The Kalman filter

was unable to be successfully implemented, and the GPS data could not be combined with the

INS data. Future work on the system would include fixing the Kalman filter, and investigating

nonlinear filters that may offer additional improvement over the linear Kalman filter.

27

VII. Appendix

A. IMU data log sample

1842,VNCMV,-5.274759E-01,-7.151102E-01,+1.306457E+00,+8.982140E-02,+1.515975E-01,-9.889581E+00,-

1.795986E-01,+2.166605E-01,+9.084704E-02,+3.184055E+02,45

2042,VNCMV,-5.238971E-01,-7.121478E-01,+1.308644E+00,+1.030171E-01,+1.572612E-01,-9.854329E+00,-

1.805358E-01,+2.170784E-01,+9.176565E-02,+3.183986E+02,42

2242,VNCMV,-5.238209E-01,-7.085825E-01,+1.309394E+00,+9.304749E-02,+1.395615E-01,-9.776874E+00,-

1.770675E-01,+2.162682E-01,+8.494401E-02,+3.183919E+02,4C

2442,VNCMV,-5.275813E-01,-7.093581E-01,+1.308815E+00,+7.542436E-02,+1.093737E-01,-9.733757E+00,-

1.773376E-01,+2.173584E-01,+8.712844E-02,+3.183853E+02,46

2642,VNCMV,-5.279517E-01,-7.131570E-01,+1.308071E+00,+6.642105E-02,+1.116978E-01,-9.784008E+00,-

1.799244E-01,+2.181875E-01,+8.413110E-02,+3.183789E+02,49

2842,VNCMV,-5.265755E-01,-7.134659E-01,+1.306714E+00,+7.675630E-02,+1.444039E-01,-9.861773E+00,-

1.805489E-01,+2.185816E-01,+8.407921E-02,+3.183725E+02,47

3042,VNCMV,-5.235814E-01,-7.112780E-01,+1.307916E+00,+9.831433E-02,+1.611955E-01,-9.883721E+00,-

1.809734E-01,+2.184756E-01,+9.345414E-02,+3.183663E+02,44

B. GPS data log sample

69435$GPGGA,224822.00,4041.98884,N,08937.03790,W,2,08,1.31,183.3,M,-33.2,M,,0000*60#57234225

70059$GPGSA,A,3,20,32,48,25,11,12,31,14,,,,,2.06,1.31,1.60*0E#57654378

70685$GPGSV,4,1,14,01,23,270,,11,08,251,10,12,08,033,36,14,43,078,19*78#57956010

71311$GPGSV,4,2,14,16,01,186,,20,27,311,26,22,24,151,08,23,02,285,26*70#58309609

71935$GPGSV,4,3,14,25,33,057,30,30,27,176,,31,82,270,26,32,54,302,31*71#58663249

72560$GPGSV,4,4,14,48,26,235,32,51,40,206,*75#59016842

73187$GPGRS,224822.00,1,-0.3,0.3,11.3,5.0,-32.2,1.5,-24.1,-6.0,,,,*72#59235274

73811$GPVTG,,T,,M,0.138,N,0.255,K,D*2E#116778602

74437$GPGGA,224823.00,4041.98874,N,08937.03785,W,2,08,0.93,182.9,M,-33.2,M,,0000*68#116960618

75060$GPGSA,A,3,20,32,48,22,25,12,31,14,,,,,1.74,0.93,1.47*04#117376617

75684$GPGSV,4,1,14,01,23,270,,11,08,251,,12,08,033,36,14,43,078,17*77#117678250

76310$GPGSV,4,2,14,16,01,186,,20,27,311,27,22,24,151,11,23,02,285,26*79#118021450

76935$GPGSV,4,3,14,25,33,057,30,30,27,176,,31,82,270,26,32,54,302,31*71#118375089

77560$GPGSV,4,4,14,48,26,235,32,51,40,206,*75#118732327

78188$GPGRS,224823.00,1,-2.0,-2.8,11.5,-13.4,8.9,1.4,-26.2,-6.9,,,,*58#118950733

78812$GPVTG,,T,,M,0.131,N,0.243,K,D*20#176380204

79438$GPGGA,224824.00,4041.98867,N,08937.03786,W,2,08,0.93,182.4,M,-33.2,M,,0000*63#176562730

80060$GPGSA,A,3,20,32,48,22,25,12,31,14,,,,,1.74,0.93,1.47*04#176978729

80685$GPGSV,4,1,14,01,23,270,,11,08,251,,12,08,033,36,14,43,078,18*78#177285036

28

REFERENCES

[1] Grewal, Mohinder S., and Angus P. Andrews. Kalman Filtering: Theory and Practice Using MATLAB. Hoboken, NJ: Wiley, 2008. Print. [2] Lin, Ching-Fang. Modern Navigation, Guidance, and Control Processing. Englewood Cliffs, NJ: Prentice Hall, 1991. Print. [3] D.H. Titterton and J.L. Weston, Strapdown Inertial Navigation Technology, 2nd Editon, The Institution of Electrical Engineers, 2004 [4] Simon, Dan, Optimal State Estimation. John Wiley & Sons, Inc., Hoboken, NJ: 2006. Print. [5] Brown, Robert Grover and Hwang, Patrick Y.C, Introduction to Random Signals and Applied Kalman Filtering. Hoboken, NJ: John Wiley & Sons, 1997. Print.